Spherical symmetric fields on torsion-free Palatini Gauss-Bonnet theory

TL;DR

This work analyzes static, spherically symmetric fields in the torsion-free Palatini Gauss-Bonnet theory in four dimensions, highlighting that the Gauss-Bonnet density is not a total derivative in this formulation. By reducing to an SO(3) symmetric sector and treating the problem as a non-canonical constrained system, the authors uncover two hidden gauge symmetries beyond diffeomorphism and Weyl invariance, confirmed through both a series analysis and linear perturbations around an exact background. They derive a reduced Lagrangian with 13 functions and show the constraint structure comprises two first-class and two second-class constraints, indicating extended gauge freedom in the extended formalism. An explicit exact background is constructed, enabling a linearized study that confirms the extra gauge symmetries and paves the way for further exploration of full solutions and perturbations beyond spherical symmetry. The results provide new insight into the gauge structure of Palatini higher-curvature gravity and motivate future work on the geometric interpretation and physical implications of these hidden symmetries.

Abstract

The Gauss-Bonnet density `a la Palatini' is not a total derivative in four dimensions. We study spherically symmetric fields for the torsion-free theory. The resulting equations are highly complicated but we show the existence of unexpected hidden gauge symmetries, beyond diffeomorphisms and Weyl transformations.